Question

15. An atom of Uranium-238 is unstable and will eventually decay (i.e., emit a particle and turn into a different element). Given an atom of Uranium-238, the time elapsed until it decays, in years, is modeled as an Exponential random variable with parameter lambda = 0.000000000155. How many years must pass for there to be a 50% chance that the Uranium atom decays?

16. The odds of a given ticket winning the Powerball lottery is p = 1/292,201,338. When the jackpot gets large, the number of tickets bought can grow quite large: in 2016, the number of tickets sold reached n = 371,000,000 one week when the jackpot had grown to over a billion dollars. The number of winners can be modeled as a Poisson random variable with parameter lambda = n*p with this many tickets sold, what is the probability that there are no winners? One winner? Two winners?

Answer 1

According to the question at is g fuen that an adom o Uranium 238 fs unstable and with eventually decay As we know Cummulatine distribution function of - Flow atelt a decay parameters DO) 2007 i is gruen as t = 0.000000000155. It can be turither as 1-55x100 $(2) 1-ě 1055X7670 ya so 0.591-6155X10" Ca. 0-155410 (1) = 0.5 pass to Hence we get 2X1.55*100 = kala) So almost u. u72x100 years as needed to . have solo chance of decay.